Simple proofs of the Siegel–Tatuzawa
and Brauer–Siegel theorems
Colloquium Mathematicum, Tome 108 (2007) no. 2, pp. 277-283
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We give a simple proof of the Siegel–Tatuzawa theorem according to which the residues at $s=1$ of the Dedekind zeta functions of quadratic number fields are effectively not too small, with at most one exceptional quadratic field. We then give a simple proof of the Brauer–Siegel theorem for normal number fields which gives the asymptotics for the logarithm of the product of the class number and the regulator of number fields.
Mots-clés :
simple proof siegel tatuzawa theorem according which residues dedekind zeta functions quadratic number fields effectively too small exceptional quadratic field simple proof brauer siegel theorem normal number fields which gives asymptotics logarithm product class number regulator number fields
Affiliations des auteurs :
Stéphane R. Louboutin 1
@article{10_4064_cm108_2_9,
author = {St\'ephane R. Louboutin},
title = {Simple proofs of the {Siegel{\textendash}Tatuzawa
} and {Brauer{\textendash}Siegel} theorems},
journal = {Colloquium Mathematicum},
pages = {277--283},
year = {2007},
volume = {108},
number = {2},
doi = {10.4064/cm108-2-9},
language = {de},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm108-2-9/}
}
Stéphane R. Louboutin. Simple proofs of the Siegel–Tatuzawa and Brauer–Siegel theorems. Colloquium Mathematicum, Tome 108 (2007) no. 2, pp. 277-283. doi: 10.4064/cm108-2-9
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